Granular activated carbon (GAC) adsorption is an important water treatment technique, but accurate, long-term prediction of trace compound adsorption has been elusive because of difficulties accounting for the competitive effects of heterogeneous natural organic matter (NOM). NOM exerts several significant competitive effects in GAC columns that can vary temporally and spatially. This study develops a 3-component GAC model, COMPSORB-GAC, that quantitatively describes trace compound adsorption in the presence of NOM with greater accuracy and elegance than previously possible. The model separately tracks adsorption of the trace compound and two fictive NOM fractions- a strongly competing and a pore blocking fraction. To accurately describe GAC column adsorption, three competitive effects were needed: direct competition for sites, intraparticle pore blockage, and external surface pore blockage. COMPSORB-GAC is the first model to incorporate these three competitive effects as explicit functions of NOM surface concentration. COMPSORB-GAC uses a moving-grid, finite-difference formulation of the governing equations that makes it possible for the first time to reflect spatial variations in adsorption parameters and to directly simulate counter-current, moving-bed reactors. A parameterization procedure consisting of independent, short-term tests with fresh and batch preloaded adsorbent was demonstrated and used to validate the modeling approach experimentally. Possible simplifications of the parameterization procedure are also presented to reduce the experimental and data fitting requirements. COMPSORB-GAC modeling showed that moving-bed GAC adsorbers can reduce carbon usage rates (CURs) for atrazine removal from a local groundwater by 45-55% in comparison to conventional fixed-bed adsorbers. The model was also used to evaluate the novel Upflow Adsorption-Ultrafiltration (UA-UF) process developed during this study to improve the performance and treatment capabilities of hybrid sorption-membrane processes. UA-UF consists of an upflow bed of granular adsorption media situated adjacent to a low-pressure membrane system. The downstream membrane allows the adsorbent to operate in a counter-current mode that increases adsorption efficiency. Concurrently, the upstream adsorbent bed provides pretreatment that improves membrane hydraulic performance. COMPSORB-GAC showed that UA-UF can reduce the CURs of current hybrid processes by more than 90%. Other advantages include small space requirements, less sludge, and the ability to regenerate and reuse the adsorbent.